
where \(\delta \)  is the number of independent channels for the experiment, \(t_{obs}\)  corresponds to the experimental observation period, \(h^2 \Omega _{GW}(f)\)  denotes the GW signal coming from the first-order phase transition and \(h^2\Omega _{Sens}(f)\)  denotes the sensitivity of experiments, such as LISA [1]}, DECIGO and BBO [2]}.
When the S/N ratio at the LISA experiment is larger than 10, we could detect the GW spectrum [3]}.
In our analysis, we take S/N>10 as a criterion for whether the GW spectrum could be detected or not.
